Some spherical analysis related to the pairs \((U(n),H_n)\) and \((U(p,q),H_n),p + q = n\)

DOI10.1007/S12044-015-0242-7zbMath1408.43008OpenAlexW1875397109MaRDI QIDQ746361

Silvina Campos, Linda Saal

Publication date: 16 October 2015

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-015-0242-7

zbMATH Keywords

Heisenberg groupspherical transform

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Analysis on other specific Lie groups (43A80)

Cites Work

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• Group representations on spaces of distributions
• The spherical transform of a Schwartz function on the Heisenberg group
• \(L^2\) spectral decomposition on the Heisenberg group associated to the action of \(\text{U}(p,q)\)
• Gelfand transforms of polyradial Schwartz functions on the Heisenberg group
• Spectra for Gelfand pairs associated with the Heisenberg group
• On the spectrum of the generalized Gelfand pair $(u(p,q), h_{n})$, $p+q=n$
• Distributions Invariant under an Orthogonal Group of Arbitrary Signature.
• A spherical transform on Schwartz functions on the Heisenberg group associated to the action of U(p,q)

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